We present a deep-learning approach for solving the problem of 2π phase ambiguities in two-dimensional quantitative phase maps of biological cells, using a multi-layer encoderdecoder residual convolutional neural network. We test the trained network, PhUn-Net, on various types of biological cells, captured with various interferometric setups, as well as on simulated phantoms. These tests demonstrate the robustness and generality of the network, even for cells of different morphologies or different illumination conditions than PhUn-Net has been trained on. In this paper, for the first time, we make the trained network publicly available in a global format, such that it can be easily deployed on every platform, to yield fast and robust phase unwrapping, not requiring prior knowledge or complex implementation. By this, we expect our phase unwrapping approach to be widely used, substituting conventional and more time-consuming phase unwrapping algorithms.